Welcome to the website of researchers working in Bilbao (either at UPV/EHU or at BCAM) in mathematical analysis, partial differential equations, inverse problems, mathematical physics, and/or related topics.
EHU, Thursday, March 12th, 12:00 - 13:00
Title: $L^p$-estimates for singular integral operators along codimension one subspaces
Mikel Florez - EHU
In this talk, we will present recent results on $L^p$-estimates for maximal directional singular integral operators in $\mathbb{R}^n$. These operators are given by a Hörmander–Mihlin multiplier on an $(n-1)$-dimensional subspace and act trivially in the perpendicular direction. The subspace is allowed to depend measurably on the first $n-1$ variables of $\mathbb{R}^n$.
Assuming the subspace is non-degenerate (in the sense that it is away from a cone around $e_n$) and the function $f$ is frequency supported in a cone away from $\mathbb{R}^{n-1}$, we establish $L^p$-bounds for these operators for $p > 3/2$. If we additionally assume that $f$ is frequency supported in a single frequency band, we are able to extend the boundedness range to $p > 1$. We will also discuss why the non-degeneracy assumption cannot in general be removed, even in the band-limited case.